On Fri, Jan 28, 2011 at 3:08 PM, Kristofer Munsterhjelm <km-el...@broadpark.no> wrote: > One could generalize Yee diagrams to other distances than Euclidean, but > AFAIK, there's a theorem that says that with any centrosymmetric > distribution, the Yee diagram for a Condorcet method is the L2 Voronoi > diagram. Warren used this to argue that Range is better than Condorcet > because it would make more sense for voters with L1 (Manhattan distance) > utility functions to yield L1 win regions (which Range does) and not L2 > (Euclidean) win regions, as Condorcet methods do.
Interesting, but wouldn't you need slightly more stringent conditions than "merely" a centrosymmetric voter distribution? For example, consider four identical gaussian distributions added together, with the peaks placed at four corners of a square. Then place four candidates, one at each peak, and rotate the candidates around the center of the square by 20 degrees or so. Now you have a centrosymmetric voter distribution and a condorcet paradox. If your condorcet method resorts to IRV to resolve the ambiguity, for example, you certainly won't get a Voroni diagram. (And I presume some of the other Condorcet methods would exibit the same behavior.) >> Given access to enough data of fully-ranked, it seems to me that it >> should be possible, especially with a Yee model, to somehow >> determine how well that model fits real life. Is a 2-d euclidean >> plane a with voters ranking based on distance from the candidates a >> reasonable model? How would you analyze this? > > You may want to check Tideman's paper "The Structure of the > Election-Generating Universe". See > http://www2.lse.ac.uk/CPNSS/projects/VPP/VPPpdf/VPPpdf_Wshop2010/Workshop%20Papers/duBaffy2010_Plassmann.pdf > . The paper suggests that a spatial model is the most accurate given the > election data examined. That paper looks interesting and very relevant, thanks! I haven't examined the other links too much yet. - Leon ---- Election-Methods mailing list - see http://electorama.com/em for list info